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## Homework Statement

Consider this matrix as the augmented matrix of a linear system. State in words the next two elementary row operations that should be performed in the process of solving the system

[tex]\begin{bmatrix}

1 & -4 & 5 & 0 & 7 \\

0 & 1 & -3 & 0 & 6 \\

0 & 0 & 1 & 0 & 2 \\

0 & 0 & 0 & 1 & -5

\end{bmatrix}[/tex]

**Solution from book**

The system is already in “triangular” form. The fourth equation is x

_{4}= –5, and the other equations do not contain the variable x

_{4}. The next two steps should be to use the variable x3 in the third equation to eliminate that variable from the first two equations. In matrix notation, that means to replace R2 by its sum with 3 times R3, and then replace R1 by its sum with –5 times R3.

## The Attempt at a Solution

I pretty much got it except this part

**R1 by its sum with –5 times R3**

That doesn't even eliminate the -4 in the first row. Shouldn't it be [tex]R_{1} \mapsto 4R_{2} - 5R_{3}[/tex]